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In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

Probability · Mathematics 2016-11-01 Yumeng Li , Ran Wang , Nian Yao , Shuguang Zhang

This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst parameter $H >1/2$ and a fast component driven by fast-varying…

Probability · Mathematics 2021-11-12 Bin Pei , Yuzuru Inahama , Yong Xu

In this article we investigate the controllability for neutral stochastic functional integro-differential equations with finite delay, driven by a fractional Brownian motion with Hurst parameter lesser than $1/2$ in a Hilbert space. We…

Probability · Mathematics 2018-09-26 Brahim Boufoussi , Soufiane Mouchtabih

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

Optimization and Control · Mathematics 2015-04-27 Viorel Barbu , Stefano Bonaccorsi , Luciano Tubaro

We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and…

Probability · Mathematics 2020-04-08 Mireia Besalú , David Márquez-Carreras , Eulàlia Nualart

In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…

Probability · Mathematics 2015-11-03 José Luís da Silva , Mohamed Erraoui , El Hassan Essaky

Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in…

Probability · Mathematics 2018-12-21 Stefano Bonaccorsi , Delio Mugnolo

The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…

Numerical Analysis · Mathematics 2024-09-11 Aurelien Junior Noupelah , Jean Daniel Mukam , Antoine Tambue

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval…

Probability · Mathematics 2012-03-08 Zdzislaw Brzezniak , Jan van Neerven , Donna Salopek

We establish Harnack inequalities for stochastic differential equations (SDEs) driven by a time-changed fractional Brownian motion with Hurst parameter $H\in(0,1/2)$. The Harnack inequality is dimension-free if the SDE has a drift which…

Probability · Mathematics 2017-09-14 Chang-Song Deng , René L. Schilling

Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in…

Probability · Mathematics 2019-02-22 Yi Chen , Jing Dong , Hao Ni

In this paper, high-order moment, even exponential moment, estimates are established for the H\"older norm of solutions to stochastic differential equations driven by fractional Brownian motion whose drifts are measurable and have linear…

Probability · Mathematics 2020-05-01 Xi-Liang Fan , Shao-Qin Zhang

In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian motion. As an application, we deduce that…

Probability · Mathematics 2007-05-23 Fabrice Baudoin , Laure Coutin

In this paper, we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$. We interpret these equations either in the sense of Young ($H>1/2$) or Stratonovich ($H=1/2$).…

Numerical Analysis · Mathematics 2026-04-01 Nahid Jamshidi , Martin Redmann

In this work we study rough differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4 and establish Varadhan's small time estimates for the density of solutions of such equations under Hormander's type…

Probability · Mathematics 2013-04-30 Fabrice Baudoin , Cheng Ouyang , Xuejing Zhang

We study the nonparametric Nadaraya-Watson estimator of the drift function for ergodic stochastic processes driven by fractional Brownian motion of Hurst parameter H > 1/2. The estimator is based on the discretely observed stochastic…

Statistics Theory · Mathematics 2022-05-03 Han Yuecai , Zhang Dingwen

In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition…

Probability · Mathematics 2007-06-13 Jorge A. Leon , Jaime San Martin

We consider Hilbert-valued evolution equations driven by H\"{o}lder paths with H\"{o}lder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not be…

Dynamical Systems · Mathematics 2019-03-06 M. J. Garrido-Atienza , B. Schmalfuss , J. Valero

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. Rates of…

Probability · Mathematics 2013-08-05 Alexandra Chronopoulou , Samy Tindel

We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,…

Probability · Mathematics 2025-10-22 Oleg Butkovsky , Khoa Lê , Leonid Mytnik